Place chopped cucumber in colander in sink and sprinkle lightly with salt.
Let drain for 20 minutes.
Meanwhile, prepare dressing and vegetables.
To Make Dressing: In a small bowl, stir together tahini, 3 tablespoons water, lemon juice, garlic, and salt to taste.
It will be as thick as mayonnaise. (Dressing may be refrigerated up to 1 week.) To Prepare Vegetables: Squeeze cucumbers dry in a clean towel.
Add green onions, radishes, and tomatoes and squeeze gently to remove excess liquid.
If not using immediately, refrigerate in towel until ready to assemble sandwiches or up to 6 hours.
Transfer to a bowl and toss together.
To Make Pita Sandwiches: Cut pita bread in half crosswise to make 2 flat rounds.
If they are not soft and pliable, place on a plate, cover with plastic wrap, and microwave on high (100%) for 30 to 50 seconds.
Spread each round with 2 tablespoons dressing.
Spread a layer of vegetables and peperoncini down the center.
Sprinkle with cheese and roll up tightly.
Repeat with remaining ingredients.
Wrap in plastic wrap and refrigerate at least 1 hour or up to 4 hours before serving.
Cut each sandwich in half to serve.
To Make Tortilla Sandwiches: Follow directions for assembling pita sandwiches. (Tortilla sandwiches may be refrigerated overnight.)